Light that bends in a way unknown to modern physics.
There are various observations that only work on the globe earth - like the position of stars (Polaris being the easiest example), and things like the sun setting, or ships dropping below the horizon. These thing prove that the Earth is a globe unless light is bending in a bizarre way that makes it only appear to be a globe.
And while you can possibly explain one of these observations as being bending light on a flat disk, you can't explain them all. You could concoct a weird set of light paths that work for observations of polaris from anywhere on the disk, but that would not explain the dip of the horizon, or the paths of the southern stars.
The term "bendy light" is a slightly humorous reference to the bizarre convolutions that light would have to go through to fit real-world observations like sunsets on the imaginary world of a flat disk. The term "bendy" is used instead of simply "bent" or "bending" to distinguish it for the minor bends of light paths we see from refraction - usually only degree or two at most near the horizon, and very little elsewhere.